Answer:
0.0286 = 2.86% probability that today is Monday.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Dressed correctly
Event B: Monday
Probability of being dressed correctly:
100% = 1 out of 4/7(mom dresses).
(0.5)^3 = 0.125 out of 3/7(toddler dresses himself). So
[tex]P(A) = 0.125\frac{3}{7} + \frac{4}{7} = \frac{0.125*3 + 4}{7} = \frac{4.375}{7} = 0.625[/tex]
Probability of being dressed correctly and being Monday:
The toddler dresses himself on Monday, so (0.5)^3 = 0.125 probability of him being dressed correctly, 1/7 probability of being Monday, so:
[tex]P(A \cap B) = 0.125\frac{1}{7} = 0.0179[/tex]
What is the probability that today is Monday?
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.0179}{0.625} = 0.0286[/tex]
0.0286 = 2.86% probability that today is Monday.
Use the given information to find the number of degrees of freedom, the critical values χ2L and χ2R, and the confidence interval estimate of σ. It is reasonable to assume that a simple random sample has been selected from a population with a normal distribution. Nicotine in menthol cigarettes 99% confidence; n=23, s=0.28 mg.
df = (Type a whole number.)
χ2L = (Round to three decimal places as needed.)
χ2R = (Round to three decimal places as needed.)
The confidence interval estimate of σ is __ mg < σ < __ mg. (Round to two decimal places as needed.)
Answer:
χ²R = 8.643
χ²L = 42.796
0.20 < σ < 0.45
Step-by-step explanation:
Given :
Sample size, n = 23
The degree of freedom, df = n - 1 = 23 - 1 = 22
At α - level = 99%
For χ²R ; 1 - (1 - 0.99)/2= 0.995 ; df = 22 ; χ²R = 8.643
For χ²L ; (1 - 0.99)/2 = 0.005 ; df = 22 ; χ²L = 42.796
The confidence interval of σ ;
s * √[(n-1)/χ²L] < σ < s * √[(n-1)/χ²R)]
0.28 * √(22/42.796) < σ < 0.28 * √(22/8.643)
0.2008 < σ < 0.4467
0.20 < σ < 0.45
At a large Midwestern university, a simple random sample of 100 entering freshmen in 1993 found that 20 of the sampled freshmen finished in the bottom third of their high school class. Admission standards at the university were tightened in 1995. In 1997, a simple random sample of 100 entering freshmen found that only 10 finished in the bottom third of their high school class. Let p 1 and p 2 be the proportions of all entering freshmen in 1993 and 1997, respectively, who graduated in the bottom third of their high school class. What is a 90% plus four confidence interval for p 1 – p 2?
Answer:
The 90% confidence interval for the difference of proportions is (0.01775,0.18225).
Step-by-step explanation:
Before building the confidence interval, we need to understand the central limit theorem and subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
p1 -> 1993
20 out of 100, so:
[tex]p_1 = \frac{20}{100} = 0.2[/tex]
[tex]s_1 = \sqrt{\frac{0.2*0.8}{100}} = 0.04[/tex]
p2 -> 1997
10 out of 100, so:
[tex]p_2 = \frac{10}{100} = 0.1[/tex]
[tex]s_2 = \sqrt{\frac{0.1*0.9}{100}} = 0.03[/tex]
Distribution of p1 – p2:
[tex]p = p_1 - p_2 = 0.2 - 0.1 = 0.1[/tex]
[tex]s = \sqrt{s_1^2+s_2^2} = \sqrt{0.04^2 + 0.03^2} = 0.05[/tex]
Confidence interval:
[tex]p \pm zs[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
90% confidence level
So [tex]\alpha = 0.1[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].
The lower bound of the interval is:
[tex]p - zs = 0.1 - 1.645*0.05 = 0.01775 [/tex]
The upper bound of the interval is:
[tex]p + zs = 0.1 + 1.645*0.05 = 0.18225 [/tex]
The 90% confidence interval for the difference of proportions is (0.01775,0.18225).
The 3rd and 6th term of a geometric progression are 9/2 and 243/16 respectively find the first term, common ratio, seventh term
Answer:
Hello,
Step-by-step explanation:
[tex]Let\ (u_n)\ the\ geometric\ progression.\\\\r\ is\ the\ common\ ratio.\\\\u_3=u_0*r^3\\u_6=u_0*r^6\\\\\dfrac{u_6}{u_3} =r^3=\dfrac{\frac{243}{16} }{\frac{9}{2} } =\dfrac{27}{8} =(\frac{3}{2} )^3\\\\\boxed{r=\dfrac{3}{2} }\\\\\\u_3=u_1*r^2 \Longrightarrow\ u_1=\dfrac{u_3}{r^2} =\dfrac{\frac{9}{2} }{(\frac{3}{2^2}) } =2\\\\\\u_7=u_6*\dfrac{3}{2} =\dfrac{729}{32}[/tex]
The quadratic equation x^2 + 3x + 50 = 0 has roots r and s. Find a quadratic equation whose roots are r^2 and s^2.
Answer:
x^2 + 91x + 2500
-----------------------------------------------------------------------------
x^2 + 3x + 50
(x-r)(x-s)
-> x^2-(r+s)x+rs
rs = 50, r + s = -3
-> (rs)^2 = 2500
(r+s)^2 = 9
-> r^2 + 2rs + s^2 = 9
-> r^2 + 2(50) + s^2 = 9
-> r^2 + s^2 + 100 = 9
-> r^2 + s^2 = -91
(x-r^2)(x-s^2)
-> x^2-(r^2+s^2)x+(rs)^2
-> x^2 - (-91)x + 2500
x^2 + 91x + 2500
Write A linear equation in standard form the passes through the points (4,-2) and (2,6)
Answer:
Step-by-step explanation:
4 x + y =
14
Use the graph of ƒ to find ƒ(2).
0.5
–8
–0.5
Does not exist
Answer:
Step-by-step explanation:
When you're looking to find things like f(2) and f(4) and f(-3000), etc. the number inside the parenthesis is an x value. Look to the graph, find that x value, and locate the y value that corresponds to it. f(2) = -8. f(-1) = 4. f(1) = -4. See?
Answer:
does not exist
Step-by-step explanation:
that what i put hope it helps
Find the sum of -3x^2-4x+3 2x^2+3
What is the slope, m, and the y-intercept of the line that is graphed below?
On a coordinate plane, a line goes through points (negative 3, 0) and (0, 3).
Answer:
Slope: 1
Y-intercept: (0,3)
Step-by-step explanation:
The y intercept is when the slope reaches the y-axis line. In this case, it is given to us. Anything that is formed like this: (0, y) is the y-intercept.
Y intercept: (0, 3)
For slope, you can use the formula rise over run. [tex]\frac{Rise}{Run}[/tex]
From the picture, I have drawn the rise over run, which is [tex]\frac{3}{3}[/tex], which is also 1.
Slope: 1
Hope this helped.
Answer: 1
Step-by-step explanation: got it right on edge
Find the circumference of the circle.
10.1 in
Hint: C = xxd
x= 3.14
A.15.857 in
B.31.714 in
C.63.428 in
D.13.24 in
Step-by-step explanation:
c=3.14×3.14×10.1
=99.58196
Use the slope-intercept form of the linear equation to write an equation of the line with given slope and y-intercept.
Slope: -6/5 y intercept (0,8)
Answer:
5y + 6x = 40
Step-by-step explanation:
hope it is well understood?
Can someone please help!!! Sec. 12.7 #78
There are 165 children taking swimming lessons at the pool. If 10 children will be assigned to each instructor, how many instructors are needed?
Answer:
17 instructors
Step-by-step explanation:
If each instructor will get 10 children, we have to divided the total number of children taking swimming lessons by the number of children assigned to each instructor (10):
165/10 = 16.5
Unfortunately, we can't have 16 and a half instructors. Since 5 children are remaining, we can round up 16.5 to 17 and get 17 instructors. This implies that 16 instructors will teach 10 children (160 in total) and 1 instructor will teach 5 children (5 in total). 160+5 = 165 total children.
The function sin 0 is reciprocal of cot 0.
True
False
Answer: False
Step-by-step explanation:
This is because sin 0 is equal to 0 but cot 0 is equal to undefined
Dr. Kingston predicted that swearing can help reduce pain. In the study, each participant was asked to plunge a hand into icy water and keep it there as long as the pain would allow. In one condition, the participants repeatedly yelled their favorite curse words while their hands were in the water. In the other condition the participants repeated a neutral word. The table below presents the amount of time that participants kept their hand in the ice in each condition.
Swear Words
Neutral Words
98
56
70
61
52
47
87
60
46
32
120
92
72
53
41
31
1. Calculate the mean for the Swear Words condition:_______________
Answer:
Step-by-step explanation:
First, we add them all up.
98+70+52+87+46+120+72+41 = 586
Now, we divide 586 by the number of things there are. 586 / 8 = 73.25.
The mean of the swear words condition is 73.25.
a-bcosc/c-bcosa=sinc/sina
=ac-b(cosc-ccosa)
=sinc/sina
What is the equation of exponential regression equation? Round all numbers you your answer to three decimal places
Given:
The given values are:
[tex]a=0.2094539899[/tex]
[tex]b=2.507467975[/tex]
[tex]r^2=0.9435996398[/tex]
[tex]r=0.9713905701[/tex]
To find:
The exponential regression equation for the given values (Rounded to three decimal places).
Solution:
The general form of exponential regression equation is:
[tex]y=a\cdot b^x[/tex] ...(i)
Where, a is the initial value and b is the growth/decay factor.
We have,
[tex]a=0.2094539899[/tex]
[tex]b=2.507467975[/tex]
Round these numbers to three decimal places.
[tex]a\approx 0.209[/tex]
[tex]b\approx 2.507[/tex]
Substitute [tex]a=0.209, b=2.507[/tex] in (i) to find the exponential regression equation.
[tex]\hat{y}=0.209\cdot 2.507^x[/tex]
Therefore, the correct option is C.
Step 3: Write the equation of the line that passes through the point (4,−1)
(
4
,
−
1
)
that is parallel to the line 2−3=9
Answer:
-
Step-by-step explanation:
-
Match each sequence below to statement that BEST fits it.
Z. The sequence converges to zero;
I. The sequence diverges to infinity;
F. The sequence has a finite non-zero limit;
D. The sequence diverges.
_______ 1. ns in (1/n)
_______2. ln(ln(ln(n)))
_______3. (ln(n))/n
_______4. n!/n^1000
Answer: hello your question is poorly written attached below is the complete question
answer:
1 ) = I (
2) = F
3) = Z
4) = D
Step-by-step explanation:
attached below is the required solution.
1 ) = I ( The sequence diverges to infinity )
2) = F ( The sequence has a finite non-zero limit )
3) = Z ( The sequence converges to zero )
4) = D ( The sequence diverges )
Alejandro wants to adopt a puppy from an animal shelter. At the shelter, he finds eight puppies that he likes: a male and female puppy from each of the four breeds of and Labrador. The puppies are each so cute that Alejandro cannot make up his mind, so he decides to pick the dog randomly. Find the probability that Alejandro chooses a .
Answer:
Hence the required probability is, 3/4
Step-by-step explanation:
At the shelter, he likes :
a male coolie, a female coolie, a male boxer, a female boxer, a male beagle, a female beagle, a male Labrador, and a female Labrador.
Let, A denote the event of selecting a male coolie and B denote the event of selecting a male Labrador.
P(A) = 1/8 = P(B)
Here the probability of selecting a puppy except A & B is,
P(AUB)c = 1 - P(AUB) = 1 - { P(A) + P(B) } = 1 - 1/8 - 1/8 = 3/4
I need help with this question
Answer:
7
This question is tying to introduce an idea that
eventually becomes a calculus question ....
(4^2 + 3(4)) - (0^2+3(0))
4 - 0
28 - 0 = 7
4
Step-by-step explanation:
Answer:
7
Step-by-step explanation:
1. Approach
The average rate of change can simply be defined as the slope of a line that passes through any two points on a coordinate plane. In this situation, one is given a function, and one is asked to find the rate of change over an interval.
Given function: [tex]f(x)=x^2+3x[/tex]
Intervale, [tex][0, 4][/tex]
This can be done by evaluating the endpoints of the interval by substituting them into the function. Then writing the resulting the form of a point on the coordinate plane ([tex]x, y[/tex]). Finally, one can find the slope of the line that passes through the points by using the following slope formula,
[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Where ([tex]x_1,y_1[/tex]) and ([tex]x_2,y_2[/tex]) are coordinate points.
2. Find the points
With the function (f(x)), substitute the end points of the itnerval ( [0, 4] ) into the function to generate coordinate points,
[tex]f(x)=x^2+3x[/tex]
[ 0, 4 ]
[tex]f(0)=(0)^2+3(0)\\=0 + 0\\ =0[/tex]
Point: (0, 0)
[tex]f(4)=(4)^2+3(4)\\= 16 + 12\\ = 28[/tex]
Point: (4, 28)
3. Find the average rate of change,
Now substitute the points the formula to find the slope, then simplify to evaluate
[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
(0, 0), (4, 28)
Substitute,
[tex]\frac{y_2-y_1}{x_2-x_1}\\\\=\frac{28-0}{4-0}\\\\=\frac{28}{4}\\\\= 7[/tex]
The average rate of change is 7.
rewrite -4<x<-1 using absolute value sign
[tex] - | 4 | < x < - |1| [/tex]
dunno if that's the desired form tough, but it states the same definition
The given inequality rewritten using absolute value sign as |-4|<x<|-1|.
What are inequalities?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
The given inequality is -4<x<-1.
An absolute value inequality is an expression with absolute functions as well as inequality signs.
Here, using absolute value sign we get
|-4|<x<|-1|
Therefore, the given inequality rewritten using absolute value sign as |-4|<x<|-1|.
To learn more about the inequalities visit:
https://brainly.com/question/20383699.
#SPJ2
You flip a coin that is not fair, the prbability of heads on each flip is 0.7. if the coin shows heads, you draw a marble from urn h with 1 blue and 4 red marbles. if the coin shows tails, you draw a marble from urn t with 3 blue and 1 red marble. Find the following probabilities:
a. The probability of choosing a red marble.
b. The probability of choosing a blue marble, given that the coin showed heads.
c. The probability that the coin showed tails, given that the marble was red.
Solution :
P(H) = 0.7 ; P(T) = 0.3
If heads, then Urn H, 1 blue and 4 red marbles.
If tails, then Urn T , 3 blue and 1 red marbles.
a).
P ( choosing a Red marble )
= P (H) x P( Red from Urn H) + P (T) x P( Red from Urn T)
[tex]$=0.7 \times \frac{4}{5} + 0.3 \times \frac{1}{4}$[/tex]
= 0.56 + 0.075
= 0.635
b). If P (B, if coin showed heads)
If heads, then marble is picked from Urn H.
Therefore,
P (Blue) [tex]$=\frac{1}{5}$[/tex]
= 0.2
c). P (Tails, if marble was red)
[tex]$=P (T/R) = \frac{P(R/T)}{P(R)} \ P(T)$[/tex]
Where P (R/T) = P ( red, if coin showed tails)
[tex]$=\frac{1}{4}$[/tex]
= 0.25 (As Urn T is chosen)
P (R) = P (Red) = 0.635 (from part (a) )
P (T) = P (Tails) = 0.3
∴ [tex]$P(T/R) = \frac{0.25 \times 0.3}{0.635}$[/tex]
= 0.118
Find the missing segment in the image below
Answer:
x = 12
Step-by-step explanation:
Missing length of the segment is the altitude of the right triangle.
Based on the geometric mean theorem, we would have the following:
h = √(ab)
Where,
h = x
a = 16
b = 9
Plug in the values:
x = √(16*9)
x = √144
x = 12
Hello people can you please help me on this I've been stuck on it for like 30 minuets now
Answer:
Step 1: Complete the first equation
0.01 is a hundredth, therefore if we have 1.86 then we have 186 hundredths.
Step 2: Complete the second equation
1.86 / 2 = 0.93
0.01 is a hundredth, therefore if we have 0.93 then we have 93 hundredths.
Step 3: Complete the third equation
1.86 / 2 = 0.93
Look at images below. : ]
Answer:
1) A
B) 5.818 stops
Step-by-step explanation:
Number One is less than or equal to 21 because the person only has 21 dollars, so she can't spend more than 21.
B can be solved through the equation by first subtracting $5, and then dividing 2.75 by 16.
How much would $200 invested at 5% interest compounded monthly be
worth after 9 years?
9514 1404 393
Answer:
$313.37
Step-by-step explanation:
The compound interest formula is used to find that value.
A = P(1 +r/12)^(12t)
P compounded monthly at annual rate r for t years.
A = $200(1 +0.05/12)^(12·9) ≈ $313.37
♥️♥️♥️♥️♥️♥️♥️♥️♥️ help me
9514 1404 393
Answer:
AC = 2.0 mm = 41.3 kgStep-by-step explanation:
The sum of torques about the pivot point is zero when the system is in equilibrium. That means the total of clockwise torques is equal to the total of counterclockwise torques. For this purpose, torque can be modeled by the product of mass and its distance from the pivot. The uniform beam can be modeled as a point mass at its center.
__
a) Let E represent the location of the center of mass of the beam. So, AE = 1.5 m. Then the distance from C to E is AC-AE = AC -1.5 and the CCW torque due to the beam's mass is (16 kg)(AC -1.5 m).
The distance from B to C is 3 m - AC, so the CW torque due to the particle at B is (7 kg)(3 -AC m)
These are equal, so we have ...
16(AC -1.5) = 7(3 -AC)
16AC -24 = 21 -7AC . . . . . eliminate parentheses
23AC = 45 . . . . . . . . . . . add 7AC+24
AC = 45/23 ≈ 1.957 . . divide by the coefficient of AC
AC ≈ 2.0 meters . . . . rounded to 1 dp
__
b) The torques in this scenario are ...
M(0.7) = 16(0.8) +7(2.3) . . . . . . AD = 0.7 m, DE = 0.8 m, DB = 2.3 m
M = 28.9/0.7 ≈ 41.286 . . . . simplify, divide by the coefficient of M
M = 41.3 kg . . . . rounded to 1 dp
_____
Additional comment
Torque is actually the product of force and distance from the pivot. Here, the forces are all downward, and due to the acceleration of gravity. The gravitational constant multiplies each mass, so there is no harm in dividing the equation by that constant, leaving the sum of products of mass and distance.
PLEASE HELP
Identify the first five terms of the sequence in which a, = 3n2 - 1.
Step-by-step explanation:
you cannot just put the actual numbers in and calculate ?
and you can't provide the correct problem statement, as it seems.
I assume you mean
an = 3n² - 1
a sequence starts with a1, so, n>=1
a1 = 3×1² - 1 = 3-1 = 2
a2 = 3×2² -1 = 3×4 - 1 = 12 - 1 = 11
a3 = 3×3² - 1 = 3×9 - 1 = 27 - 1 = 26
a4 = 3×4² - 1 = 3×16 - 1 = 48 - 1 = 47
a5 = 3×5² - 1 = 3×25 - 1 = 75 - 1 = 74
there, that is all there is to it. you really needed help with that ?
Drag each equation to the correct location on the table.
Match the equations with the value of x that makes them true.
5x - 2x - 4 = 5
5x - (3x - 1) = 7
x + 2x + 3 = 9
2(2x - 3) = 6
4x - (2x + 1) = 3
5(x + 3) = 25
x = 2
X = 3
Answer:
The answer to your questions are given below.
Step-by-step explanation:
To answer the question given above, we shall determine the value of x in each equation. This can be obtained as follow:
5x - 2x - 4 = 5
3x - 4 = 5
Collect like terms
3x = 5 + 4
3x = 9
Divide both side by 3
x = 9/3
x = 3
5x - (3x - 1) = 7
Clear the bracket
5x - 3x + 1 = 7
2x + 1 = 7
Collect like terms
2x = 7 - 1
2x = 6
Divide both side by 2
x = 6/2
x = 3
x + 2x + 3 = 9
3x + 3 = 9
Collect like terms
3x = 9 - 3
3x = 6
Divide both side by 3
x = 6/3
x = 2
2(2x - 3) = 6
Clear the bracket
4x - 6 = 6
Collect like terms
4x = 6 + 6
4x = 12
Divide both side by 4
x = 12/4
x = 3
4x - (2x + 1) = 3
Clear the bracket
4x - 2x - 1 = 3
2x - 1 = 3
Collect like terms
2x = 3 + 1
2x = 4
Divide both side by 2
x = 4/2
x = 2
5(x + 3) = 25
Clear the bracket
5x + 15 = 25
Collect like terms
5x = 25 - 15
5x = 10
Divide both side by 5
x = 10/5
x = 2
SUMMARY:
x = 2
x + 2x + 3 = 9
4x - (2x + 1) = 3
5(x + 3) = 25
x = 3
5x - 2x - 4 = 5
5x - (3x - 1) = 7
2(2x - 3) = 6
A computer is selling for $883 the finance value is $1077.26 under an 11% simple interest loan what is the length of the loan
Answer:
The length of the loan was 2 years.
Step-by-step explanation:
Given that a computer is selling for $ 883, and the finance value is $ 1077.26 under an 11% simple interest loan, to determine what is the length of the loan, the following calculation must be performed:
883 x 0.11 = 97.13
(1077.26 - 883) / 97.13 = X
194.26 / 97.13 = X
2 = X
Therefore, the length of the loan was 2 years.
